Hello!
Hmm, I've never had to get a bike set up, having always had someone on hand to build it for me.
My first instinct would be Cycleworks, on Lawrence Street, just because they are probably the friendliest shop, and I think, a co-op. No idea what they'll charge though. There's also Cycle Heaven, Bishopthorpe Road, Bob Trotters on Lord Mayor's Walk, and Fulford Cycles, on Fulford Road, a bit further out than the others. Probably worth ringing round and asking if they'll do it, and for how much.
Another thought is Bike Rescue, on Terry Avenue (down by the river, on a little industrial unit). They recycle and sell bikes, but I think they also take in servicing jobs, so they might be able to help - it might depend on how busy they are, they are mostly volunteers and so on. Drop by or give them a call.
http://www.yorkrecycling.net/index.php?id=84
And once you've got your bike set up, keep an eye on the events section, we try and get a ride out once a month or so.
If you want any advice on good routes around, or out of, town, ask away here, or PM me...